Central Limit Theorem in Holder spaces in the terms of majorizing measures
arXiv:1409.6054
Abstract
We obtain some sufficient conditions for the Central Limit Theorem for the random processes (fields) with values in the separable part of Holder space in the modern terms of majorizing (minorizing) measures, belonging to X.Fernique and M.Talagrand. We introduce a new class of Banach spaces-rectangle Holder spaces and investigate CLT in this spaces via the fractional order Sobolev-Grand Lebesgue norms. Our further considerations based on the improvement of the L.Arnold and P.Imkeller generalization of the classical Garsia-Rodemich-Rumsey inequality, which allow us to reduce degree of the distance in the important particular cases.
arXiv admin note: substantial text overlap with arXiv:1302.3202, arXiv:1301.0132
References in corpus (8)
- Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)
- Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
- Asymptotic exponential bounds for MLE deviation under minimal conditions via classical and generic chaining methods
- Module of continuity for the functions belonging to the Sobolev-Grand Lebesgue Spaces
- H{ö}lder continuity of random processes
- A counterexample to a hypothesis of light tail of maximum distribution for continuous random processes with light finite-dimensional tails
- Continuity of functions belonging to the fractional order Sobolev-Grand Lebesgue Spaces
- Uniform measures on the arbitrary compact metric spaces, with applications
Cited by in corpus (4)
- Factorable continuity of random fields, with quantitative estimation
- Each Random Variable in separable Banach Space belongs to the Domain of Definition of some inverse to compact linear non-random operator
- Problem of Estimation of Fractional Derivative for a Spectral Function of Gaussian Stationary Processes
- Strengthening of weak convergence for Radon measures in separable Banach spaces